A popular style of ornamental design involves filling a container region with a number of small decorative elements. The decorative elements are simple geometric forms, often stylized flora, spirals, or other abstract shapes. The elements are large enough that they can be appreciated individually, but they work together to communicate the overall container shape. Typically, they also form a cohesive stylistic family.
There has been a moderate amount of past research in computer graphics, particularly in the field of non-photorealistic rendering, on the generation of packings or mosaics. Most techniques pack elements via rigid motions, leading to high uniformity but insufficient variety. Other work involves distributing small geometric elements to create textures or mosaics. A. Hausner describes in Simulating decorative mosaics, Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '01, pp. 573-580. ACM, New York, N.Y., USA, 2001. doi: 10.1145/383259.383327 for example, a variant of Lloyd's method to distribute square tiles, oriented relative to a vector field, in a simulation of traditional mosaics. Subsequent work has generalized the approach to families of distinct element shapes and incorporated an FFT-based image correlation step to produce more uniform negative space. See, e.g., S. Hiller, H. Hellwig, and O. Deussen, Beyond Stippling—Methods for Distributing Objects on the Plane, Computer Graphics Forum, 2003. doi: 10.1111/1467-8659.00699; and, K. Dalal, A. W. Klein, Y. Liu, and K. Smith, A spectral approach to NPR packing, Proceedings of the 4th International Symposium on Non-photorealistic Animation and Rendering, NPAR '06, pp. 71-78. ACM, New York, N.Y., USA, 2006. doi: 10.1145/1124728.1124741.
A separate thread of research treats the placement of elements as a form of example-based texture synthesis; see, e.g., T. Hurtut, P.-E. Landes, J. Thollot, Y. Gousseau, R. Drouillhet, and J.-F. Coeurjolly, Appearance-guided synthesis of element arrangements by example, Proceedings of the 7th International Symposium on Non-Photorealistic Animation and Rendering, NPAR '09, pp. 51-60. ACM, New York, N.Y., USA, 2009, doi: 10.1145/1572614.1572623; and Z. AlMeraj, C. S. Kaplan, and P. Asente, Patch-based geometric texture synthesis, Proceedings of the Symposium on Computational Aesthetics, CAE '13, pp. 15-19. ACM, New York, N.Y., USA, 2013. doi: 10.1145/2487276.2487278. In these techniques, the goal is to reproduce the statistical properties of an input texture, including the irregular spacing between elements. T. Ijiri, R. Měch, T. Igarashi, and G. S. P. Miller, in An example-based procedural system for element arrangement, Comput. Graph. Forum, 27:429-436, 2008, propose a growth model in which elements can be oriented relative to a vector field and constrained by boundary curves. In these cases, as with the techniques based on Lloyd's method, elements are placed via translation and rotation, with no provision for deformation.
Other work includes Jigsaw Image Mosaics (JIMs) which pack elements into a container region tightly, leaving no negative space at all. See, e.g., J. Kim, F. Pellacini, Jigsaw image mosaics, Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '02, pp. 657-664. ACM, New York, N.Y., USA, 2002. doi: 10.1145/566570.566633. The JIMs are constructed via an optimization that permits limited degrees of overlap and deformation. Computation of tilings of the plane based on user-supplied shapes is described in: C. S. Kaplan and D. H. Salesin, Escherization, Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '00, pp. 499-510. ACM Press/Addison-Wesley Publishing Co., New York, N.Y., USA, 2000. doi: 10.1145/344779.345022. These techniques do not consider the design opportunities offered by flow or control of negative space.
A distinct category of past research seeks to develop explicit procedural models for authoring decorative patterns. A set of design principles for decorative art that includes: repetition, balance, and conformation to geometric constraints, is articulated along a grammar-like system for laying out floral ornaments by M. T. Wong, D. E. Zongker, and D. H. Salesin, in Computer-generated floral ornament, Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '98, pp. 423-434. ACM, New York, N.Y., USA, 1998. doi: 10.1145/280814.280948. Another example is DecoBrush, in which ornamental elements are deformed along line art as described by J. Lu, C. Barnes, C. Wan, P. Asente, R. Mech, and A. Finkelstein in DecoBrush: Drawing structured decorative patterns by example, ACM Trans. Graph., 33(4):90:1-90:9, July 2014. doi: 10.1145/2601097.2601190. The PATEX system as described by P. Guerrero, G. Bernstein, W. Li, and N. J. Mitra in PATEX: Exploring pattern variations, ACM Trans. Graph., 35(4):48:1-48:13, July 2016. doi: 10.1145/2897824.2925950 preserves high-level geometric relationships like symmetry and repetition while ornamental designs are edited.
Other related research includes that pertaining to packing individual letter-forms or blocks of text into container regions, such as, for example, constructing calligrams by filling a container with a small number of letters, making up one or two words. See, e.g., J. Xu and C. S. Kaplan, Calligraphic packing, Proceedings of Graphics Interface 2007, GI '07, pp. 43-50. ACM, New York, N.Y., USA, 2007. doi: 10.1145/1268517.1268527; and C. Zou, J. Cao, W. Ranaweera, I. Alhashim, P. Tan, A. Sheffer, and H. Zhang, Legible compact calligrams, ACM Trans. Graph., 35(4):122:1-122:12, July 2016. doi: 10.1145/2897824.2925887. The goal is to balance between consuming the container space and preserving legibility. Another example is deformation of lines of text to fit along streamlines in a container such as described by R. Maharik, M. Bessmeltsev, A. Sheffer, A. Shamir, and N. Carr, Digital micrography, ACM SIGGRAPH 2011 Papers, SIGGRAPH '11, pp. 100:1-100:12. ACM, New York, N.Y., USA, 2011. doi: 10.1145/1964921.1964995.
Finally, some recent work has explored the elaboration of ornamental patterns on surfaces, under constraints imposed by fabrication. For example, W. Chen, X. Zhang, S. Xin, Y. Xia, S. Lefebvre, and W. Wang, Synthesis of filigrees for digital fabrication, ACM Trans. Graph., 35(4):98:1-98:13, July 2016, doi: 10.1145/2897824.2925911 described a method to synthesize filigree patterns. J. Zehnder, S. Coros, and B. Thomaszewski, Designing structurally sound ornamental curve networks, ACM Trans. Graph., 35(4):99:1-99:10, July 2016, doi: 10.1145/2897824.2925888 proposed semi-automated tools for deforming ornamental curves to cover a surface. In both cases, the layout of elements must be computed to satisfy both aesthetic and structural goals-most obviously, elements must overlap to produce a connected result that will hold together when 3D printed.
While the above-described work provides a variety of techniques for generating artistic works there remains a need for computerized methods and systems that can generate ornamental designs employing a container filled with irregularly shaped elements that are visually pleasing and that permit the elements to be appreciated individually while communicating the overall shape of the container.